{
 "metadata": {
  "name": "",
  "signature": "sha256:7a030b3958f7b74d79872b35fc06ab05d559866ad61fbe63ac645f31b96b569c"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Demonstrating that \"rank ordering\" of predicted probabilites is all that matters for ROC/AUC"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Normal process: predict probabilities, calculate AUC, plot ROC"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# read the data from titanic.csv into a DataFrame\n",
      "import pandas as pd\n",
      "url = 'https://raw.githubusercontent.com/justmarkham/DAT7/master/data/titanic.csv'\n",
      "titanic = pd.read_csv(url, index_col='PassengerId')\n",
      "\n",
      "# fill NAs for Age\n",
      "titanic.Age.fillna(titanic.Age.mean(), inplace=True)\n",
      "\n",
      "# define Pclass/Parch as the features and Survived as the response\n",
      "feature_cols = ['Pclass', 'Parch', 'Age']\n",
      "X = titanic[feature_cols]\n",
      "y = titanic.Survived\n",
      "\n",
      "# split the data into training and testing sets\n",
      "from sklearn.cross_validation import train_test_split\n",
      "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)\n",
      "\n",
      "# fit a logistic regression model\n",
      "from sklearn.linear_model import LogisticRegression\n",
      "logreg = LogisticRegression(C=1e9)\n",
      "logreg.fit(X_train, y_train)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "LogisticRegression(C=1000000000.0, class_weight=None, dual=False,\n",
        "          fit_intercept=True, intercept_scaling=1, penalty='l2',\n",
        "          random_state=None, tol=0.0001)"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# calculate predicted probabilities\n",
      "y_pred_prob1 = logreg.predict_proba(X_test)[:, 1]\n",
      "y_pred_prob1[:10]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "array([ 0.52501831,  0.19102245,  0.52729118,  0.19102245,  0.72728774,\n",
        "        0.24370353,  0.48165812,  0.63755459,  0.69316123,  0.19102245])"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# show predicted probabilities in a histogram\n",
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "plt.hist(y_pred_prob1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "(array([  8.,  66.,  27.,  16.,  27.,  32.,   8.,  24.,   9.,   6.]),\n",
        " array([ 0.07652196,  0.15504032,  0.23355867,  0.31207703,  0.39059539,\n",
        "         0.46911375,  0.54763211,  0.62615047,  0.70466882,  0.78318718,\n",
        "         0.86170554]),\n",
        " <a list of 10 Patch objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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q1vVY4FeAPwbesk5qeg5wSjd94bT31Zg1nbRg+qnMX3vQa00L1vss8Eng5evk8xsAu6Zd\ny4Q1bQRuA07v5k/tu6ZF618MfKbvmoBZ4J0H9xHwPWBDzzX9BfCObvpJ4+ynlfbQx7m46BJgB0BV\n3QBsTDKzwnZXXFdV3VtVNwEPTrmWSWq6vqoOdLM3AKevg5p+vGD20cB3+66p8ybgo8C9U65n0rom\nPjNhyjW9CvhYVX0DoKrWy+e3sL4Pr4Oavg2c3E2fDHyvqh7quaZzgD0AVfVV4Kwkjz3cRlca6ONc\nXLTUOtMOqvV40dOkNb0WuGaqFY1ZU5JLk9wBfAq4vO+akjyO+R/+v+0WrcWBoHH2VQHP7f5FvibJ\nk9dBTb8EbEqyJ8lNSV69DmoCIMmJwG8CH1sHNb0PeEqSbwG3AG9eBzXdArwMIMl5wOMZkZ0rubAI\nxv9FWtxrmfYv4Ho80jt2TUkuAF4DPG965QBj1lRVO4GdSX4V+BDz//71WdO7ge1VVUnC2vSKx6nr\nS8AZVfWTJBcBO4EtPdf0KOBc5k8vPhG4PskXquprPdZ00EuAf6uq+6dUy0Hj1PR24OaqGiR5IrA7\nydOr6oc91vQu4D1J9gK3AnuBnx3uDSsN9G8CZyyYP4P5vzSHW+f0btk0jVPXWhurpu5A6PuAC6vq\nvvVQ00FV9fkkG5L8YlV9r8eafhn4yHyWcypwUZIHq2rXlGoaq66Fv/xV9akkf5NkU1V9v6+amO8F\nfreqfgr8NMnngKcD0wr0SX6mXsH0h1tgvJqeC/wJQFXdneS/me+43NRXTd3P02sOznc1/ddht7rC\ngf0NwN3MD+wfx+iDouezNgdFR9a1YN1Z1uag6Dj76kzmD5ScP+16JqjpiTxyeuu5wN1917Ro/Q8C\nL1sn+2pmwb46D7hnHdS0FfgM8wfhTmS+p/fkvj8/4BTmDzyesE4+u78ErlzwOX4D2NRzTacAx3XT\nrwP+fuR2V6Gwi5i/YvQu4Ipu2euB1y9Y573d67cA5077AxynLuA05nsvB4D7gP8BHt1zTe/vfsj3\ndl83roP99AfAV7p6Pg88q++aFq27JoE+5r56Q7evbgb+gzX4wzzm799bmT/T5Vbg8nVS0zbgH9fi\ncxvzszsVuLrLqFuBV62Dmp7TvX4n8ycAnDJqm15YJEmN8BF0ktQIA12SGmGgS1IjDHRJaoSBLkmN\nMNAlqREGuiQ1wkCXpEb8L7sbICaqnt6xAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1786f5c0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# calculate AUC\n",
      "from sklearn import metrics\n",
      "metrics.roc_auc_score(y_test, y_pred_prob1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "0.68400493421052633"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot ROC curve\n",
      "fpr, tpr, thresholds = metrics.roc_curve(y_test, y_pred_prob1)\n",
      "plt.plot(fpr, tpr)\n",
      "plt.xlim([0.0, 1.0])\n",
      "plt.ylim([0.0, 1.0])\n",
      "plt.xlabel('False Positive Rate (1 - Specificity)')\n",
      "plt.ylabel('True Positive Rate (Sensitivity)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<matplotlib.text.Text at 0x18988c50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HUDd8LVbytVjJ12L1VbPGsA8wNyLmRcQSYDQwokWZI4EbASJiEtBP0uZVjKnL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\nE4OZmZVxYjAzszJODGZmVsaJwczMyvx/PIKdvbRzXrgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1787b8d0>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Take the square root of predicted probabilities (makes them all bigger)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# change the predicted probabilities\n",
      "import numpy as np\n",
      "y_pred_prob2 = np.sqrt(y_pred_prob1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# here are the old ones (y_pred_prob1)\n",
      "y_pred_prob1[:10]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "array([ 0.52501831,  0.19102245,  0.52729118,  0.19102245,  0.72728774,\n",
        "        0.24370353,  0.48165812,  0.63755459,  0.69316123,  0.19102245])"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# here are the new ones (y_pred_prob2)\n",
      "y_pred_prob2[:10]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "array([ 0.72458147,  0.43706115,  0.72614818,  0.43706115,  0.85281167,\n",
        "        0.49366338,  0.69401594,  0.79847016,  0.83256305,  0.43706115])"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# you can see the histogram changed\n",
      "plt.hist(y_pred_prob2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(array([  2.,   9.,  57.,  30.,  14.,  23.,  39.,  11.,  27.,  11.]),\n",
        " array([ 0.27662603,  0.34179152,  0.40695701,  0.47212251,  0.537288  ,\n",
        "         0.60245349,  0.66761899,  0.73278448,  0.79794997,  0.86311547,\n",
        "         0.92828096]),\n",
        " <a list of 10 Patch objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1787f588>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# the AUC did not change\n",
      "metrics.roc_auc_score(y_test, y_pred_prob2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "0.68400493421052633"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# the ROC curve did not change\n",
      "fpr, tpr, thresholds = metrics.roc_curve(y_test, y_pred_prob2)\n",
      "plt.plot(fpr, tpr)\n",
      "plt.xlim([0.0, 1.0])\n",
      "plt.ylim([0.0, 1.0])\n",
      "plt.xlabel('False Positive Rate (1 - Specificity)')\n",
      "plt.ylabel('True Positive Rate (Sensitivity)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.text.Text at 0x18ea0fd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HUDd8LVbytVjJ12L1VbPGsA8wNyLmRcQSYDQwokWZI4EbASJiEtBP0uZVjKnL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\nE4OZmZVxYjAzszJODGZmVsaJwczMyvx/PIKdvbRzXrgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x18e9e4e0>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Make small predicted probabilities smaller, and make big predicted probabilities bigger"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y_pred_prob3 = np.where(y_pred_prob1 > 0.5, np.sqrt(y_pred_prob1), y_pred_prob1**2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# you can see these are different from y_pred_prob1 and y_pred_prob2\n",
      "y_pred_prob3[:10]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "array([ 0.72458147,  0.03648958,  0.72614818,  0.03648958,  0.85281167,\n",
        "        0.05939141,  0.23199454,  0.79847016,  0.83256305,  0.03648958])"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# the histogram changed\n",
      "plt.hist(y_pred_prob3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "(array([ 101.,   32.,   26.,    0.,    0.,    0.,    0.,   19.,   28.,   17.]),\n",
        " array([ 0.00585561,  0.09809815,  0.19034068,  0.28258322,  0.37482575,\n",
        "         0.46706829,  0.55931082,  0.65155336,  0.74379589,  0.83603843,\n",
        "         0.92828096]),\n",
        " <a list of 10 Patch objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x18e93048>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# the AUC did not change\n",
      "metrics.roc_auc_score(y_test, y_pred_prob3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "0.68400493421052633"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# the ROC curve did not change\n",
      "fpr, tpr, thresholds = metrics.roc_curve(y_test, y_pred_prob3)\n",
      "plt.plot(fpr, tpr)\n",
      "plt.xlim([0.0, 1.0])\n",
      "plt.ylim([0.0, 1.0])\n",
      "plt.xlabel('False Positive Rate (1 - Specificity)')\n",
      "plt.ylabel('True Positive Rate (Sensitivity)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "<matplotlib.text.Text at 0x192a8da0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HUDd8LVbytVjJ12L1VbPGsA8wNyLmRcQSYDQwokWZI4EbASJiEtBP0uZVjKnL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\nE4OZmZVxYjAzszJODGZmVsaJwczMyvx/PIKdvbRzXrgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x190b9390>"
       ]
      }
     ],
     "prompt_number": 16
    }
   ],
   "metadata": {}
  }
 ]
}